JP2005309999A - Device and method for evaluating swirling flow - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a device for evaluating swirling flows capable of precisely determining a swirling flow by use of velocity vectors at each node (coordinate point) even if there exist other flows or a plurality of swirling flows. <P>SOLUTION: The device for evaluating swirling flows is used that comprises a characteristic equation calculating part 3 and a swirling axis calculating part 4. Based on data about the velocities of fluid at coordinate points, the characteristic equation calculating part 3 calculates a characteristic value from a characteristic equation about the coordinate points and the velocity data. When the characteristic value is a complex number, the swirling axis calculating part 4 assumes the imaginary part of the complex number as a swirling function, calculates a coordinate point that provides the maximum value of the swirling function, and sets the coordinate point that provides the maximum value as the position of the swirling axis of the swirling flow in the fluid. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a swirl flow evaluation device and a swirl flow evaluation method, and more particularly to a swirl flow evaluation device and a swirl flow evaluation method for evaluating swirl flow in a fluid flow.

  A swirling flow is known as a type of fluid flow. FIG. 1 is a diagram illustrating an example of a fluid flow in a state of only a swirl flow. This figure shows velocity vectors at each of a plurality of nodes (coordinate points) in one of the swirling planes of the swirling flow (planes perpendicular to the swirling axis of the swirling flow). The direction of the velocity vector is indicated by the direction of the arrow, and the magnitude of the velocity vector is indicated by the length of the arrow. As shown in the figure, in the swirl flow, the fluid rotates around the swivel axis P0.

  FIG. 2 is a diagram illustrating an example of a fluid flow in a state where the swirl flow and the uniform flow are combined. This figure shows velocity vectors at each of a plurality of nodes (coordinate points) when a uniform horizontal flow from left to right in the figure is added to the swirling flow of FIG. Thus, if there is a uniform flow in addition to the swirling flow, the existence of the swirling flow cannot be visually recognized.

  A technique capable of accurately identifying a swirling flow using a velocity vector at each node (coordinate point) is desired. There is a demand for a technique that can accurately identify a swirling flow even when other flows exist. Even when other flows and a plurality of swirling flows exist, a technique capable of accurately identifying these swirling flows is required.

  As a related technique, D.C. Sujudi, R.A. Haimes, “Identification of Swirling Flow in 3-D Vector Fields”, 12th AIAA Compute Fluid Dyn Conf 1995 Part 2, (1995), p. 792-799 (Non-Patent Document 1) discloses a method for evaluating swirling flow. This method first calculates the eigenvalue of the velocity gradient tensor. Next, if the eigenvalue is a complex number, a coordinate point having a velocity of 0 around the point on the turning plane is searched. Then, the coordinate point whose speed is 0 is set as the position of the turning axis. However, in this method, when a uniform flow exists, it is difficult to obtain the turning axis.

  As a related technique, R.K. C. Strawn, D.W. N. Kenwright, J.M. Ahmad, “Computer Visualization of Vortex Wake System”, AIAA (1999), vol. 7 (No. 4), p. 511-512 (Non-Patent Document 2) discloses another swirling flow evaluation method. This method calculates the vorticity ω. A coordinate point representing the maximum of the vorticity ω is set as the position of the turning axis. However, the vorticity ω represents an angular velocity (twice) in an arbitrary flow pattern, not limited to a swirling flow. Therefore, a flow having a vorticity ω does not always indicate a swirling flow. That is, having the vorticity ω is not a sufficient condition as a swirling flow.

  As a related technique, S.M. Kida, H.M. Miura, “Identification and analysis of vital structure”, E.M. J. et al. Mech. B / Fluids, (1998), vol. 17 (No. 4), p471-488 (Non-patent Document 3) discloses still another swirling flow evaluation method. This method determines the pivot axis from the flow of pressure hessian and transient / velocity gradient tensor. However, not only speed data but also pressure data is required, and the calculation is complicated. When analyzing from experimental data, it is difficult to obtain pressure data having a sufficient number of coordinate points necessary for the analysis.

D. Sujudi, R.A. Haimes, “Identification of Swirling Flow in 3-D Vector Fields”, 12th AIAA Compute Fluid Dyn Conf 1995 Part 2, (1995), p. 792-799 R. C. Strawn, D.W. N. Kenwright, J.M. Ahmad, “Computer Visualization of Vortex Wake System”, AIAA (1999), vol. 7 (No. 4), p. 511-512 S. Kida, H.M. Miura, “Identification and analysis of vital structure”, E.M. J. et al. Mech. B / Fluids, (1998), vol. 17 (No. 4), p471-488

  Accordingly, an object of the present invention is to provide a swirl flow evaluation device and a swirl flow evaluation method capable of accurately identifying a swirl flow using velocity vectors at each node (coordinate points).

  Another object of the present invention is to provide a swirl flow evaluation device and a swirl flow evaluation method capable of accurately identifying a swirl flow even when other flows or a plurality of swirl flows exist.

  Still another object of the present invention is to provide a swirl flow evaluation device and a swirl flow evaluation method capable of accurately determining the presence or absence of a swirl flow.

  Another object of the present invention is to provide a swirl flow evaluation device and a swirl flow evaluation method capable of distinguishing a swirl flow having a swirl axis (vortex axis) from a swirl flow not having the swirl axis. .

  Hereinafter, means for solving the problem will be described using the numbers and symbols used in the best mode for carrying out the invention. These numbers and symbols are added in parentheses in order to clarify the correspondence between the description of the claims and the best mode for carrying out the invention. However, these numbers and symbols should not be used for interpreting the technical scope of the invention described in the claims.

Therefore, in order to solve the above-mentioned problem, the swirling flow evaluation device of the present invention includes an eigen equation calculation unit (3) and a swirl axis calculation unit (4). The eigen equation calculation unit (3) calculates an eigen value (λ) from an eigen equation relating to the coordinate point (x) and the velocity data (v) based on the fluid velocity data (v) at the coordinate point (x). When the eigenvalue (λ) is a complex number (λR ± iφ), the turning axis calculation unit (4) uses the imaginary part (φ) of the complex number (λR ± iφ) as the turning function (φ), and the turning function (φ) The coordinate point (x0) that gives the maximum value is calculated, and the coordinate point (x0) that gives the maximum value (φ0) is taken as the position of the swirling axis (P) of the swirling flow in the fluid.
Here, based on the velocity data (v) at the coordinate point (x), Taylor expansion of the velocity is performed in the moving coordinate system moving at the velocity of the evaluation target coordinate point (x), and the second and subsequent higher-order terms are ignored. The velocity gradient tensor obtained by doing

  In the above-described swirl flow evaluation device, the swivel axis calculation unit (4) calculates the maximum value (φ0) in the swivel function (φ), and sets the maximum value (φ0) as the angular velocity on the swivel axis (P).

  The above-described swirl flow evaluation device is a swirl line calculation unit (6) for calculating a swirl line (S) indicating the swirl flow based on the eigenvector (ξ) and swirl function (φ) calculated from the eigen equation. And a display unit (7) for displaying the turning line (S).

  In the swirl flow evaluation device, the swirl axis calculation unit (4) further determines that there is no swirl flow when the eigenvalue (λ) is not a complex number (λR ± iφ).

In the swirl flow evaluation device, the swirl axis calculation unit (4) further determines that there is no clear swirl axis (P) when there is no maximum value (φ0) that satisfies the predetermined condition.
The absence of a clear swivel axis means that the center of the swirl flow is swirling around a finite region rather than an axis.

  In order to solve the above problem, a fluid simulation apparatus of the present invention includes an analysis device (2) that calculates velocity data at each of a plurality of coordinate points indicating positions in a fluid based on input of data related to the fluid; The swirl flow evaluation device (1) according to any one of the above paragraphs.

  In order to solve the above problems, the swirling flow evaluation method of the present invention is executed by a swirling flow evaluation device (1) including an eigen equation calculation unit (3) and a swirling axis calculation unit (4). (A) Based on the fluid velocity data (v) at the coordinate point (x) output from the communication line or the storage device, the eigen equation calculation unit (3) uses the coordinate point (x) and velocity data (v) A step of calculating an eigenvalue (λ) from an eigen equation relating to (b), and (b) when the swing axis calculation unit (4) is a complex number (λR ± iφ), the imaginary part of the complex number (λR ± iφ) Using (φ) as a turning function (φ), a coordinate point (x0) giving a maximum value (φ0) in the turning function (φ) is calculated, and a coordinate point (x0) giving a maximum value (φ0) is turned in the fluid. And a step of setting the position of the swirl axis (S) of the flow.

  In the above swirl flow evaluation method, (c) the swivel axis calculation unit (4) calculates the maximum value (φ0) in the swivel function (φ), and the maximum value (φ0) is the angular velocity on the swivel axis (P). The following step is further included.

  In the above swirl flow evaluation method, (d) calculating a swirl line (S) indicating the swirl flow based on the eigenvector (ξ) and swirl function (φ) calculated from the eigen equation; And (e) displaying a turning line (S).

  In order to solve the above problems, the computer program of the present invention is caused to be executed by a swirling flow evaluation device (1) including an eigen equation calculation unit (3) and a swirl axis calculation unit (4). (A) Based on the fluid velocity data (v) at the coordinate point (x) output from the communication line or the storage device, the eigen equation calculation unit (3) uses the coordinate point (x) and velocity data (v) A step of calculating an eigenvalue (λ) from an eigen equation relating to (b), and (b) when the swing axis calculation unit (4) is a complex number (λR ± iφ), the imaginary part of the complex number (λR ± iφ) Using (φ) as a turning function (φ), a coordinate point (x0) giving a maximum value (φ0) in the turning function (φ) is calculated, and a coordinate point (x0) giving a maximum value (φ0) is turned in the fluid. The swirl flow evaluation device (1) is caused to execute a swirl flow evaluation method including a step of setting the position of the swirl axis (P) of the flow.

  In the above computer program, the coordinate point (x) is a plurality of coordinate points (x). (A) Step: (a1) For each of a plurality of coordinate points (x), the eigen equation calculation unit (3) determines the coordinate point (x) and the velocity data (v) based on the coordinate point (x) and the velocity data (v). Calculating the eigenvalue (λ) from the eigenequation for the velocity data (v). (B) In step (b1), when the eigenvalue (λ) is a complex number (λR ± iφ) for each of the plurality of coordinate points (x), the turning axis calculation unit (4) determines that the complex number (λR ± iφ) A step of calculating a coordinate point (x0) that gives the maximum value (φ0) in the turning function (φ), with the imaginary part (φ) as a turning function (φ), and (b2) a coordinate point that gives the maximum value (φ0) When there are a plurality of (x0), each of the plurality of coordinate points (x0) giving the maximum value (φ0) is set to the position of the swirling axis (P) of the swirling flow in the fluid.

  In the above computer program, (c) the turning axis calculation unit (4) calculates a maximum value (φ0) in the turning function (φ), and sets the maximum value (φ0) as an angular velocity on the turning axis (p). Is further provided.

  In the above computer program, (d) calculating a swirling line (S) indicating the swirling flow based on the eigenvector (ξ) and swirling function (φ) calculated from the eigen equation; (e) And a step of displaying a turning line (S).

  In the above computer program, in step (b), (b3) the swing axis calculation unit (4) determines that the fluid has no swirl flow when the eigenvalue (λ) is not a complex number (λR ± iφ). Comprising steps.

  In the above computer program, (b) step includes (b4) when the swing axis calculation unit (4) does not have a maximum value (φ0) that satisfies a predetermined condition, the fluid has a clear swing axis (P). A step of determining that there is not.

  In order to solve the above-described problems, the computer program of the present invention is a computer program that is executed by a simulation apparatus including an analysis device (2) and a swirl flow evaluation device (1). (F) The analysis device (2) calculates the velocity data (v) at the coordinate point (x) indicating the position in the fluid based on the input of the data related to the fluid, and (g) the swirl flow evaluation device ( 1) causes a simulation apparatus to execute a fluid simulation method including the step of executing the computer program according to any one of the above paragraphs.

  According to the present invention, even when other flows or a plurality of swirling flows are present, the swirling flow can be accurately identified using the velocity vector at each node (coordinate point). The presence or absence of a swirling flow and the presence or absence of a swirling flow having a swirling axis (vortex axis) can be accurately determined.

  Hereinafter, embodiments of a swirl flow evaluation device and a swirl flow evaluation method of the present invention will be described with reference to the accompanying drawings. First, the configuration of the embodiment of the swirling flow evaluation device of the present invention will be described.

  FIG. 3 is a block diagram showing the configuration of the embodiment of the swirling flow evaluation device of the present invention. The swirl flow evaluation device 1 is an information processing device exemplified by a workstation or a personal computer. The swirl flow evaluation device 1 includes a speed data acquisition unit 2 as a program, an eigen equation calculation unit 3, a swivel axis calculation unit 4, a swirl line calculation unit 6, and a display unit 7. Furthermore, a speed database 8 and a result database 9 are provided as data and programs. The speed database 8 and the result database 9 may be integrated.

The velocity data acquisition unit 2 performs numerical analysis based on computational fluid dynamics based on input of data related to the fluid. Then, at each of a plurality of coordinate points x (three-dimensional: x ₁ , x ₂ , x ₃ ) indicating the position in the fluid, velocity data v (three-dimensional vector: v ₁ , v ₂ , v ₃ ) of the fluid. Is calculated. The calculated data is stored in the speed database 8. You may output directly to the eigenequation calculation part 3.

The fluid velocity data v (three-dimensional vector: v ₁ , v ₂ , v ₃ ) at each of a plurality of coordinate points x (three-dimensional: x ₁ , x ₂ , x ₃ ) is communicated to the swirling flow evaluation device 1. You may acquire from the other memory | storage device (not shown) connected by the circuit | line (not shown) and the other apparatus (not shown) on a network. In this case, another device (not shown) may have the function of the speed data acquisition unit 2 or other simulation devices related to the flow of fluid (example: ship, wind generator, turbine, It may be a fluid machine, an aircraft, a chemical / nuclear power plant simulation apparatus).

  The speed database 8 stores the speed data v calculated by the speed data acquisition unit 2 in association with the coordinate point x. For data acquired from another storage device (not shown) or a device on the network (not shown), the velocity data v may be stored in association with the coordinate point x.

The eigen equation calculation unit 3 acquires the velocity data v associated with the coordinate point x from the velocity data acquisition unit 2 or the velocity database 8. Based on the fluid velocity data v at the coordinate point x, the eigenvalue λ and the eigenvector ξ (ξ ₁ , ξ ₂ , ξ ₃ ) are calculated from the eigen equation relating to the coordinate point x and the velocity data v. Since the coordinate point x and the velocity data v are three-dimensional data, three eigenvalues λ (λ ₁ , λ ₂ , λ ₃ ) are also calculated. The calculation result is output to the turning axis calculation unit 4.

When the eigenvalue λ is a complex number represented by λ _R ± iφ (i is an imaginary number), the turning axis calculation unit 4 defines the imaginary part φ of the complex number λ _R ± iφ as a turning function φ. A coordinate point x0 when the turning function φ (x ₁ , x ₂ , x ₃ ) takes a maximum value φ0 is calculated. The coordinate point x0 is defined as the position of the turning axis P of the swirling flow in the fluid.

  The turning axis calculation unit 4 further calculates a maximum value φ0 in the turning function φ. The maximum value φ0 is defined as the angular velocity on the turning axis P. These eigenvalue λ, eigenvector ξ, turning function φ, maximum value φ0 = angular velocity, and position x0 of the turning axis P are stored in the result database 9.

  The result database 9 includes an eigenvalue λ and an eigenvector ξ calculated by the eigen equation calculation unit 3, a turning function φ calculated by the turning axis calculation unit 4, a position x 0 of the turning axis P, and a maximum value calculated by the angular velocity calculation unit 5. φ0 = angular velocity is stored in association with the coordinate point x and velocity data.

,
Based on the eigenvector ξ and the turning function φ, the turning line calculation unit 6 calculates a turning line S indicating the turning flow. The calculation result is output to the display unit 7. The display unit 7 displays the turning line S on the display based on the calculation result.

  FIG. 4 is a block diagram showing the hardware configuration of the embodiment of the swirling flow evaluation device of the present invention. The swirling flow evaluation device 1 includes a central processing unit (CPU) 11, a first memory 12, a second memory 13, an input / output unit 14, and a display 15 that are connected to each other via a bus 16.

  The speed data acquisition unit 2, the eigen equation calculation unit 3, the turning axis calculation unit 4, the turning line calculation unit 6, the display unit 7, the speed database 8, and the result database 9 are the second memory exemplified by the hard disk (HD). 13. Among them, the speed data acquisition unit 2, eigen equation calculation unit 3, swivel axis calculation unit 4, swirl line calculation unit 6, and display unit 7 are exemplified in a random access memory (RAM) during the operation of the swirl flow evaluation device 1. And is executed by the CPU 11. The speed database 8 and the result database 9 are appropriately read and written by the CPU 11. If necessary, input from the input / output unit 14 exemplified by a communication port or a keyboard (including input from an external device via a communication line) is performed.

  This swirl flow evaluation device may be included in a part of another simulation device related to the fluid flow. The position and angular velocity of the swirling flow can be grasped more accurately, and the simulation accuracy related to the fluid flow can be improved. Examples of such a simulation apparatus include a ship, a wind power generator, a turbine, an aircraft, and a chemical / nuclear power plant.

  Next, the operation of the embodiment of the swirling flow evaluation device of the present invention (the swirling flow evaluation method of the present invention) will be described. FIG. 5 is a flowchart showing the operation of the embodiment of the swirling flow evaluation device of the present invention.

(1) Step S01:
The velocity data acquisition unit 2 performs numerical analysis by computational fluid dynamics for a predetermined fluid. By numerical analysis, at each of a plurality of coordinate points x (three-dimensional: x ₁ , x ₂ , x ₃ ) indicating the position in the fluid, the fluid velocity data v (three-dimensional vector: v ₁ , v ₂ , v ₃ ) ₃ ) is calculated. The calculated data is output to the eigen equation calculation unit 3.
The result of numerical analysis that has already been performed may be received from another storage device (not shown) and output to the eigen equation calculation unit 3.

(2) Step S02
The eigen equation calculation unit 3 acquires fluid velocity data v for each of a plurality of coordinate points x in the fluid. At each of the plurality of coordinate points x, the following eigen equation (1) is established and the calculation is executed. However, in the execution of the calculation, the fluid continuity condition of Equation (2) is added.

ただし、
ｖ_ｉ：速度データｖの速度成分（ｉ＝１、２、３）
ｘ_ｊ：座標点ｘの座標成分（ｊ＝１、２、３）
λ：固有値
δ_ｉｊ：クロネッカーデルタ（Ｋｒｏｎｅｃｋｅｒ Ｄｅｌｔａ、ｉ＝ｊのとき１、その他のとき０）
である。

However,
v _i : Speed component of speed data v (i = 1, 2, 3)
x _j : Coordinate component of coordinate point x (j = 1, 2, 3)
λ: eigenvalue δ _ij : Kronecker delta (Kronecker Delta, 1 when i = j, 0 otherwise)
It is.

ただし、
ｘ＝（ｘ_１、ｘ_２、ｘ_３）
ｃ_ｊ∈Ｒ：定数（ｊ＝１、２、３）
λ_ｊ：算出された固有値λ（ｊ＝１、２、３）
ξ^（ｊ）＝（ξ^（ｊ） _１、ξ^（ｊ） _２、ξ^（ｊ） _３）：算出された固有ベクトルξ（ｊ＝１、２、３）
である。 As a result of the calculation, the following solution can be obtained.

However,
x = (x ₁ , x ₂ , x ₃ )
c _j ∈ R: constant (j = 1, 2, 3)
λ _j : calculated eigenvalue λ (j = 1, 2, 3)
ξ ^(j) = (ξ ^(j) ₁ , ξ ^(j) ₂ , ξ ^(j) ₃ ): calculated eigenvector ξ (j = 1, 2, 3)
It is.

(3) Step S03
In the equation (3), the three eigenvalues λ (λ _j (j = 1, 2, 3)) include two values: (i) all real numbers, and (ii) one real number and the other two complex numbers. There may be cases.
For each of a plurality of coordinate points x in the fluid, in the case of (i), it is determined that there is no swirling flow involving the fluid in the vicinity of the coordinate points. In the case of (ii), it is determined that there is a swirling flow.
If all of the plurality of coordinate points x are (i) (step S03: No), the process proceeds to step S08. In other cases (step S03: Yes), the process proceeds to step 04 below for the coordinate point x that has become (ii).

ただし、
φ＝φ（ｘ_１、ｘ_２、ｘ_３）
＝φ（ｒ、θ、ｚ）（円筒座標系）
＞０
ｉ：虚数
である。 (4) Step S04
In the case of (ii), the following eigenvalue λ is expressed as follows.

However,
φ = φ (x ₁ , x ₂ , x ₃ )
= Φ (r, θ, z) (cylindrical coordinate system)
> 0
i: Imaginary number.

The turning axis calculation unit 4 defines the imaginary part φ of the complex number λ _R ± iφ as a turning function φ. The turning function φ (x ₁ , x ₂ , x ₃ ) = φ (r, θ, z) (cylindrical coordinate system) where the coordinate point x 0 (x ₁₀ , x ₂₀ , x ₃₀ ) = φ (r ₀ , θ ₀ , z ₀ ) is calculated. Examples of the method for calculating the coordinate point x0 include a method for obtaining the change of the function obtained by differentiating the turning function φ and a method for obtaining the maximum value of the turning function φ. The coordinate point x0 is defined as the position of the turning axis P of the swirling flow in the fluid.

  Here, when there are a plurality of coordinate points giving the maximum value, it is determined that a plurality of swirl flows exist. Each of the plurality of coordinate points giving the maximum value is defined as the position of a plurality of swirl axes P1, P2,... Corresponding to a plurality of swirl flows.

(5) Step S05
When there is no clear maximum value, it is determined that the swirl flow does not have a clear swirl axis (vortex axis) (flow forcibly swung). Here, the clear maximum value is a maximum value that satisfies a predetermined standard. An example of the predetermined reference is that the difference between the maximum value and the average value is equal to or greater than a predetermined value. If there is no clear maximum value (step S05: No), the process proceeds to step S08. In other cases (step S05: Yes), the process proceeds to the following step 06.

(6) Step S06
The turning axis calculation unit 4 further calculates a maximum value φ0 in the turning function φ. For example, when the coordinate point x0 is obtained from a change in the function obtained by differentiating the turning function φ, the maximum value φ0 can be calculated by substituting the value of the coordinate point X0 into the turning function φ. When the coordinate point x0 is obtained from the maximum value of the turning function φ, the maximum value is the maximum value φ0. The maximum value φ0 is defined as the angular velocity on the turning axis P. In the case where there are a plurality of pivot axes P1, P2,..., The maximum value is similarly obtained and the angular velocity is defined.
These eigenvalue λ, eigenvector ξ, turning function φ, maximum value φ0 = angular velocity, and position x0 of the turning axis P are stored in the result database 9.

(7) Step S07
Based on the eigenvector ξ and the turning function φ, the turning line calculation unit 6 calculates a turning line S indicating the turning flow.
When the eigenvalues λ ₁ and λ ₂ are complex numbers (equation (4)), the eigenvectors ξ ⁽¹⁾ and ξ ⁽²⁾ corresponding to the eigenvalues λ ₁ and λ ₂ are also complex numbers. The eigenvector ξ is expressed as follows.

ただし、
ｉ：虚数
である。

However,
i: Imaginary number.

  When the eigenvalue λ of the equations (4) and (5) and the eigenvectors ξ of the equations (6) and (7) are substituted into the equation (3), the turning line S (the locus of the coordinate point x) is It is calculated as follows. When there are a plurality of turning axes P1, P2,..., The same calculation is performed for these turning lines S1, S2,.

ただし、ｃ_ｊ＝１（ｊ＝１、２、３）

Where c _j = 1 (j = 1, 2, 3)

(8) Step S08
The display unit 7 displays the turning line S (S1, S2,...) On the display 15 based on the calculation result of step S07. Alternatively, if all of the plurality of coordinate points x are (i) in step S03, it is displayed that there is no swirling flow. Alternatively, if the swirl flow does not have a clear swirl axis (vortex axis) in step S05, it is displayed that there is no swirl axis.

  As described above, the operation of the embodiment of the swirling flow evaluation device of the present invention is executed.

FIG. 6 is a graph showing the results of evaluation of Burgers vortex velocity data by the swirl flow evaluation device of the present invention. The vertical axis represents the value of the turning function φ (r, θ, z), and the horizontal axis represents the value of r. The graph shows a change in the turning function φ in a predetermined direction (θ is fixed) in a predetermined turning plane (z is fixed).
In this case, φ is the maximum value φ0 at the position of r = r0. That is, the position of r = r0 is the position of the turning axis P, and φ = φ0 is the angular velocity on the turning axis P. That is, in the present invention, the position of the swirling flow P is defined as r0, and the angular velocity is defined as φ0. This position and angular velocity were confirmed to be consistent with the Burgers vortex value obtained with a mathematical exact solution.

  It was also confirmed that this result was consistent with all of the plurality of coordinate points x where the turning function φ exists.

  FIG. 7 is a view of FIG. 6 viewed from the direction of the turning axis P. FIG. Here, the darker the color, the larger the turning function φ. There is a maximum value at the center, which is the position of the turning axis P at r = r0 in FIG. That is, by obtaining the distribution of the value of the turning function φ, the position of the turning axis can be easily found visually.

FIG. 8 is a graph showing another result of evaluating the Burgers vortex velocity data with the swirl flow evaluation device of the present invention. The three axes are the eigenvectors ξ ⁽¹⁾ , ξ ⁽²⁾ and ξ ⁽³⁾ , respectively. The graph shows the turning line S (the locus of the coordinate point x). This trajectory coincides with the value of Burgers vortex obtained by other methods known in the art.

  In the present invention, the usefulness of the present invention has been proved as described above in the Burgers vortex, which is well known in hydrodynamics as a vortex model. In other words, it is theoretically proved that the eigenvalue is not a complex number only on the swivel axis, but is a complex number around the swivel axis, and the imaginary part of the complex number of the eigenvalue becomes the maximum value on the swivel axis. It was. This imaginary part is defined as a turning function, which indicates that it is a physical quantity of angular velocity.

The present invention is applicable not only to other Burgers vortices but also to other general flows. An example is shown in FIG.
FIG. 9 is a diagram illustrating a result of evaluating an example of a fluid flow in a state where the swirl flow and the uniform flow in the predetermined swirl plane illustrated in FIG. 2 are combined by the swirl flow evaluation device of the present invention. . This figure shows velocity vectors at each of a plurality of nodes (coordinate points) when a uniform horizontal flow from left to right in the figure is added to the swirling flow of FIG. In addition to these, the position of the turning axis P0 and the turning line S in the turning flow shown in FIG. 1 are shown. The position of the turning axis P0 and the turning line S coincide with those obtained by other conventionally known methods.

  As described above, the swirling flow evaluation device according to the present invention has a method in which the swirling axis P is determined from the maximum value of the swirling function φ, and there is a uniform flow in addition to the swirling flow (the speed is not zero even with the swirling axis P). However, the position of the turning axis P0 can be correctly identified and the turning line S can be calculated. And the existence can be clearly indicated.

  According to the present invention, it is possible to distinguish between a swirling flow having a clear swirling axis (vortex axis) and a swirling flow that does not (clearly swirling flow). In the case of having a clear swivel axis, the swivel function has a convex distribution with peaks around the swivel axis, but in a forced swirl flow, the swivel function does not become maximal on the swivel axis.

  According to the present invention, it is possible to accurately calculate a swirl flow using a relatively simple calculation method, even when other flows or a plurality of swirl flows exist, using velocity vectors at each node (coordinate points).

  The swirling flow evaluation apparatus and swirling flow evaluation method of the present invention can be used by being incorporated in a simulation related to fluid flow in a ship, a wind power generator, a turbine, a fluid machine, an aircraft, a plant, or the like. In that case, the position and angular velocity of the swirling flow can be grasped more accurately, and the simulation accuracy can be improved.

FIG. 1 is a diagram illustrating an example of a fluid flow in a state of only a swirl flow. FIG. 2 is a diagram illustrating an example of a fluid flow in a state where the swirl flow and the uniform flow are combined. FIG. 3 is a block diagram showing the configuration of the embodiment of the swirling flow evaluation device of the present invention. FIG. 4 is a block diagram showing the hardware configuration of the embodiment of the swirling flow evaluation device of the present invention. FIG. 5 is a flowchart showing the operation of the embodiment of the swirling flow evaluation device of the present invention. FIG. 6 is a graph showing the results of evaluating Burgers vortex velocity data with the swirl flow evaluation device of the present invention. FIG. 7 is a view of FIG. 6 viewed from the direction of the turning axis P. FIG. FIG. 8 is a graph showing another result of evaluating Burgers vortex velocity data by the swirl flow evaluation device of the present invention. FIG. 9 is a diagram showing a result of evaluating an example of the fluid flow in which the swirl flow and the uniform flow shown in FIG. 2 are combined by the swirl flow evaluation device of the present invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Swirling flow evaluation apparatus 2 Speed data acquisition part 3 Eigen equation calculation part 4 Turning axis calculation part 6 Turning line calculation part 7 Display part 8 Speed database 9 Result database 11 CPU
12 First memory 13 Second memory 14 Input / output unit 15 Display

Claims (16)

Based on fluid velocity data at the coordinate point, an eigen equation calculation unit that calculates an eigen value from an eigen equation relating to the coordinate point and the velocity data;
When the eigenvalue is a complex number, using the imaginary part of the complex number as a turning function, a coordinate point that gives a maximum value in the turning function is calculated, and the coordinate point that gives the maximum value is the position of the turning axis of the swirling flow in the fluid A swirl flow evaluation device comprising: a swirl axis calculation unit. The swirl flow evaluation device according to claim 1,
The swirl axis calculation unit further calculates the maximum value in the swirl function, and sets the maximum value as an angular velocity on the swirl axis. In the swirl flow evaluation device according to claim 2,
A swirl flow evaluation device, further comprising: a swirl line calculation unit that calculates a swirl line indicating the swirl flow based on the eigenvector calculated from the eigen equation and the swirl function; and a display unit that displays the swirl line. The swirl flow evaluation device according to claim 1,
The swirl axis calculation unit further determines that the fluid has no swirl flow when the eigenvalue is not a complex number. The swirl flow evaluation device according to claim 1,
The swirl axis calculation unit further determines that the fluid does not have a clear swirl axis when there is no maximum value that satisfies a predetermined condition. An analysis device that calculates velocity data at each of a plurality of coordinate points indicating a position in the fluid based on input of data relating to the fluid;
A fluid simulation device comprising: the swirl flow evaluation device according to any one of claims 1 to 5. A swirl flow evaluation method executed by a swirl flow evaluation device including an eigen equation calculation unit and a swirl axis calculation unit,
(A) the eigen equation calculation unit calculates an eigen value from an eigen equation relating to the coordinate point and the velocity data based on fluid velocity data at the coordinate point;
(B) When the swing axis calculation unit calculates the coordinate point that gives the maximum value in the turning function, with the imaginary part of the complex number as the turning function, when the eigenvalue is a complex number, the coordinate point that gives the maximum value is calculated A swirl flow evaluation method comprising the step of setting a swirl axis position of the swirl flow in the fluid. In the evaluation method of the swirl flow according to claim 7,
(C) The swirl axis calculation unit further includes a step of calculating the maximum value in the swirl function, and setting the maximum value as an angular velocity on the swirl axis. The swirling flow evaluation method according to claim 7 or 8,
(D) calculating a swirl line indicating the swirl flow based on the eigenvector calculated from the eigen equation and the swirl function;
(E) A method of evaluating swirling flow, further comprising the step of displaying the swirling line. A computer program to be executed by a swirl flow evaluation device including an eigen equation calculation unit and a swirl axis calculation unit,
(A) the eigen equation calculation unit calculates an eigen value from an eigen equation relating to the coordinate point and the velocity data based on fluid velocity data at the coordinate point output from a communication line or a storage device;
(B) When the swing axis calculation unit calculates the coordinate point that gives the maximum value in the turning function, with the imaginary part of the complex number as the turning function, when the eigenvalue is a complex number, the coordinate point that gives the maximum value is calculated A computer program that causes the swirl flow evaluation device to execute a swirl flow evaluation method. The computer program according to claim 10.
The coordinate points are a plurality of coordinate points,
The step (a) includes:
(A1) For each of the plurality of coordinate points, the eigen equation calculation unit includes a step of calculating eigen values from eigen equations relating to the coordinate points and the velocity data based on the coordinate points and the velocity data,
The step (b)
(B1) For each of the plurality of coordinate points, when the eigenvalue is a complex number, the turning axis calculation unit calculates a coordinate point that gives a maximum value in the turning function by using the imaginary part of the complex number as a turning function. Steps,
(B2) When there are a plurality of coordinate points giving the maximum value, each of the plurality of coordinate points giving the maximum value is set as the position of the swirling axis of the swirling flow in the fluid. The computer program according to claim 10 or 11,
(C) The computer program further comprising a step in which the turning axis calculation unit calculates the maximum value in the turning function and sets the maximum value as an angular velocity on the turning axis. The computer program according to claim 12, wherein
(D) calculating a swirl line indicating the swirl flow based on the eigenvector calculated from the eigen equation and the swirl function;
(E) A computer program further comprising the step of displaying the turning line. The computer program according to claim 10.
The step (b)
(B3) A computer program comprising a step of determining that the fluid does not have a swirl flow when the eigenvalue is not a complex number. The computer program according to claim 10.
In the step (b),
(B4) A computer program comprising a step of determining that the fluid does not have a clear swing axis when the swing axis calculation unit does not have the maximum value that satisfies a predetermined condition. A computer program to be executed by a simulation device including an analysis device and a swirl flow evaluation device,
(F) the analysis device calculating velocity data at a coordinate point indicating a position in the fluid based on an input of data relating to the fluid;
(G) The swirl flow evaluation device includes a step of executing the computer program according to any one of claims 10 to 15. A computer program that causes the simulation device to execute a fluid simulation method.

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